Effect of Modulation on the Onset of Convection in a Sparsely Packed Porous Layer

1990 ◽  
Vol 112 (3) ◽  
pp. 685-689 ◽  
Author(s):  
N. Rudraiah ◽  
M. S. Malashetty
Keyword(s):  
Porous Layer ◽  
Applied Field ◽  
Critical Rayleigh Number ◽  
Time Dependent ◽  
Brinkman Model ◽  
Onset Of Convection ◽  
Flow Limit ◽  
The Stability ◽  
Boussinesq Fluid ◽  
Degenerate Cases

The stability of a Boussinesq fluid-saturated horizontal porous layer heated from below is examined when the applied temperature gradient is the sum of a steady component and a time-dependent sinusoidal component. The Brinkman model is employed and only infinitesimal disturbances are considered. A perturbation solution as a function of the applied field is obtained. The critical Rayleigh number is obtained for several cases depending on the frequency of oscillations and it is found that it is possible to advance or delay the onset of convection by thermal modulation of the wall temperature. The Darcy limit and viscous flow limit are obtained as degenerate cases.

scholarly journals Effect of modulation on the onset of thermal convection

1969 ◽  
Vol 35 (2) ◽  
pp. 243-254 ◽  
Author(s):  
Giulio Venezian
Keyword(s):  
Temperature Field ◽  
Applied Field ◽  
Critical Rayleigh Number ◽  
Perturbation Expansion ◽  
Horizontal Layer ◽  
Time Dependent ◽  
Steady Temperature ◽  
Onset Of Convection ◽  
Time Modulation ◽  
The Stability

The stability of a horizontal layer of fluid heated from below is examined when, in addition to a steady temperature difference between the walls of the layer, a time-dependent sinusoidal perturbation is applied to the wall temperatures. Only infinitesimal disturbances are considered. The effects of the oscillating temperature field are treated by a perturbation expansion in powers of the amplitude of the applied field. The shift in the critical Rayleigh number is calculated as a function of frequency, and it is found that it is possible to advance or delay the onset of convection by time modulation of the wall temperatures.

Stability and Convection in Impulsively Heated Porous Layers

2008 ◽  
Vol 130 (11) ◽  
Author(s):  
M. J. Kohl ◽  
M. Kristoffersen ◽  
F. A. Kulacki
Keyword(s):  
Porous Medium ◽  
Rayleigh Number ◽  
Heated Surface ◽  
Critical Rayleigh Number ◽  
Axisymmetric Flow ◽  
Temperature Fluctuations ◽  
Lower Surface ◽  
Onset Of Convection ◽  
Upward Moving ◽  
The Stability

Experiments are reported on initial instability, turbulence, and overall heat transfer in a porous medium heated from below. The porous medium comprises either water or a water-glycerin solution and randomly stacked glass spheres in an insulated cylinder of height:diameter ratio of 1.9. Heating is with a constant flux lower surface and a constant temperature upper surface, and the stability criterion is determined for a step heat input. The critical Rayleigh number for the onset of convection is obtained in terms of a length scale normalized to the thermal penetration depth as Rac=83/(1.08η−0.08η2) for 0.02<η<0.18. Steady convection in terms of the Nusselt and Rayleigh numbers is Nu=0.047Ra0.91Pr0.11(μ/μ0)0.72 for 100<Ra<5000. Time-averaged temperatures suggest the existence of a unicellular axisymmetric flow dominated by upflow over the central region of the heated surface. When turbulence is present, the magnitude and frequency of temperature fluctuations increase weakly with increasing Rayleigh number. Analysis of temperature fluctuations in the fluid provides an estimate of the speed of the upward moving thermals, which decreases with distance from the heated surface.

Throughflow effects on convective instability in superposed fluid and porous layers

1991 ◽  
Vol 231 ◽  
pp. 113-133 ◽  
Author(s):  
Falin Chen
Keyword(s):  
Porous Layer ◽  
Convective Instability ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Vertical Direction ◽  
Single Layer ◽  
Layer Depth ◽  
Onset Of Convection ◽  
Precise Control ◽  
Porous Layers

We implement a linear stability analysis of the convective instability in superposed horizontal fluid and porous layers with throughflow in the vertical direction. It is found that in such a physical configuration both stabilizing and destabilizing factors due to vertical throughflow can be enhanced so that a more precise control of the buoyantly driven instability in either a fluid or a porous layer is possible. For ζ = 0.1 (ζ, the depth ratio, defined as the ratio of the fluid-layer depth to the porous-layer depth), the onset of convection occurs in both fluid and porous layers, the relation between the critical Rayleigh number Rcm and the throughflow strength γm is linear and the Prandtl-number (Prm) effect is insignificant. For ζ ≥ 0.2, the onset of convection is largely confined to the fluid layer, and the relation becomes Rcm ∼ γ2m for most of the cases considered except for Prm = 0.1 with large positive γm where the relation Rcm ∼ γ3m holds. The destabilizing mechanisms proposed by Nield (1987 a, b) due to throughflow are confirmed by the numerical results if considered from the viewpoint of the whole system. Nevertheless, from the viewpoint of each single layer, a different explanation can be obtained.

Experimental investigation of convective stability in a superposed fluid and porous layer when heated from below

1989 ◽  
Vol 207 ◽  
pp. 311-321 ◽  
Author(s):  
Falin Chen ◽  
C. F. Chen
Keyword(s):  
Porous Layer ◽  
Fluid Layer ◽  
Critical Rayleigh Number ◽  
Linear Stability Theory ◽  
Convective Stability ◽  
Onset Of Convection ◽  
Temperature Distributions ◽  
Critical Wavelength ◽  
Crystal Film ◽  
Flux Curve

Experiments have been carried out in a horizontal superposed fluid and porous layer contained in a test box 24 cm × 12 cm × 4 cm high. The porous layer consisted of 3 mm diameter glass beads, and the fluids used were water, 60% and 90% glycerin-water solutions, and 100% glycerin. The depth ratio ď, which is the ratio of the thickness of the fluid layer to that of the porous layer, varied from 0 to 1.0. Fluids of increasingly higher viscosity were used for cases with larger ď in order to keep the temperature difference across the tank within reasonable limits. The top and bottom walls were kept at different constant temperatures. Onset of convection was detected by a change of slope in the heat flux curve. The size of the convection cells was inferred from temperature measurements made with embedded thermocouples and from temperature distributions at the top of the layer by use of liquid crystal film. The experimental results showed (i) a precipitous decrease in the critical Rayleigh number as the depth of the fluid layer was increased from zero, and (ii) an eightfold decrease in the critical wavelength between ď = 0.1 and 0.2. Both of these results were predicted by the linear stability theory reported earlier (Chen & Chen 1988).

Onset of cellular convection in a salinity gradient due to a lateral temperature gradient

1974 ◽  
Vol 63 (3) ◽  
pp. 563-576 ◽  
Author(s):  
C. F. Chen
Keyword(s):  
Salinity Gradient ◽  
Critical Rayleigh Number ◽  
Time Dependent ◽  
Field Equations ◽  
Stable States ◽  
Critical Wavelength ◽  
Wide Range ◽  
Random Disturbances ◽  
Dependent Flow ◽  
The Stability

We consider the two-dimensional problem of a linearly stratified salt solution contained between two infinite vertical plates. The fluid and the plates are initially at the same temperature. At t = 0, one of the plates is given a step increase in temperature, while the other is maintained at the initial temperature. A time-dependent basic flow is thus generated. The stability of such a time-dependent flow is analysed using an initial value problem approach to the linear stability equations. The method consists of initially distributing small random disturbances of given vertical wavelength throughout the fluid. The disturbances may be in the vorticity, temperature or salinity. The linearized field equations are integrated numerically. The growth or decay of the kinetic energy of the perturbation delineates unstable and stable states. Results have been obtained for a wide range of gap widths. The critical wavelength and the critical Rayleigh number compare favourably with those obtained previously in both physical and numerical experiments.

Stability of a Horizontal Porous Layer with Timewise Periodic Boundary Conditions

1979 ◽  
Vol 101 (2) ◽  
pp. 244-248 ◽  
Author(s):  
B. Chhuon ◽  
J. P. Caltagirone
Keyword(s):  
Porous Layer ◽  
Periodic Boundary ◽  
Lower Boundary ◽  
Periodic Boundary Conditions ◽  
Temperature Oscillation ◽  
Linear Stability Theory ◽  
Onset Of Convection ◽  
Thermal Signal ◽  
Periodic Temperature ◽  
The Stability

The stability of a horizontal porous layer bounded by two impermeable planes is investigated. A time dependent periodic temperature profile is imposed on the lower boundary while the upper plane is kept at constant temperature. Starting from the preconvective temperature distribution, and using the linear stability theory, a criterion for the onset of convection is defined as a function of the perturbation wavenumber and of the amplitude and frequency of the temperature oscillation. Experimental work with a setup allowing both the amplitude and the frequency of the thermal signal to vary is done. Finally, the equations are also solved numerically and the results are compared to the previous ones. A synthesis of all results is included.

Effect of modulation on the onset of thermal convection in a viscoelastic fluid-saturated sparsely packed porous layer

1990 ◽  
Vol 68 (2) ◽  
pp. 214-221 ◽  
Author(s):  
N. Rudraiah ◽  
P. V. Radhadevi ◽  
P. N. Kaloni
Keyword(s):  
Porous Layer ◽  
Viscoelastic Fluid ◽  
Phase Modulation ◽  
Applied Field ◽  
Temperature Modulation ◽  
Elastic Parameters ◽  
Oldroyd Model ◽  
Maximum Range ◽  
Periodic Temperature ◽  
The Stability

The stability of a Boussinesq viscoelastic fluid-saturated horizontal porous layer, when the boundaries of the layer are subjected to periodic temperature modulation, is analyzed. The Darcy–Forchheimer–Brinkman–Oldroyd model is employed and only infinitesimal disturbances are considered. Three cases of the oscillating temperature field were examined: (a) symmetric, so that the wall temperatures are modulated in phase, (b) asymmetric, corresponding to out-of-phase modulation, and (c) only the bottom wall is modulated. Perturbation solution in powers of the amplitude of the applied field is obtained. The effect of the frequency of modulation on the stability is clearly shown. Possibilities of the occurrence of subcritical instabilities are also discussed. It is shown that an increase in the elastic parameters A1 and A2 has a stabilizing influence. An increase in the Prandtl number destabilizes the system for small values of the frequency but stabilizes the systems for large values of the frequency. It is shown that the system is most stable when the boundary temperatures are modulated out of phase. The maximum range of ε when subcritical instabilities exist is also determined.

Stability of Thermal Convection in a Vertical Porous Layer

1987 ◽  
Vol 109 (4) ◽  
pp. 889-893 ◽  
Author(s):  
L. P. Kwok ◽  
C. F. Chen
Keyword(s):  
Rayleigh Number ◽  
Linear Stability ◽  
Porous Layer ◽  
Thermal Convection ◽  
Variable Viscosity ◽  
Critical Rayleigh Number ◽  
Linear Stability Theory ◽  
Lateral Heating ◽  
The Stability ◽  
Allowable Temperature

Experiments were carried out to study the stability of thermal convection generated in a vertical porous layer by lateral heating in a tall, narrow tank. The porous medium, consisting of glass beads, was saturated with distilled water. It was found that the flow became unstable at a critical ΔT of 29.2°C (critical Rayleigh number of 66.2). Linear stability analysis was applied to study the effects of the Brinkman term and of variable viscosity separately using a quadratic relationship between the density and temperature. It was found that with the Brinkman term, no instability could occur within the allowable temperature difference across the tank. With the effect of variable viscosity included, linear stability theory predicts a critical ΔT of 43.4°C (Rayleigh number of 98.3).

Onset of Convection in a Fluid Saturated Porous Layer Overlying a Solid Layer Which is Heated by Constant Flux

1999 ◽  
Vol 121 (4) ◽  
pp. 1094-1097 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Rayleigh Number ◽  
Porous Layer ◽  
Critical Rayleigh Number ◽  
Hydrothermal Systems ◽  
Solid Layer ◽  
Onset Of Convection ◽  
Constant Flux ◽  
Saturated Porous Layer ◽  
Bottom Heating ◽  
Temperature Heating

The thermoconvective stability of a porous layer overlying a solid layer is important in seafloor hydrothermal systems and thermal insulation problems. The case for constant flux bottom heating is considered. The critical Rayleigh number for the porous layer is found to increase with the thickness of the solid layer, a result opposite to constant temperature heating.

scholarly journals Thermal convection for a Darcy-Brinkman rotating anisotropic porous layer in local thermal non-equilibrium

2021 ◽  
Author(s):  
Florinda Capone ◽  
Jacopo A. Gianfrani
Keyword(s):  
Natural Convection ◽  
Rayleigh Number ◽  
Porous Layer ◽  
Nonlinear Stability ◽  
Critical Rayleigh Number ◽  
Vertical Axis ◽  
Linear Instability ◽  
Brinkman Model ◽  
Linear Instability Analysis ◽  
Non Equilibrium

AbstractThe onset of natural convection in a fluid-saturated anisotropic porous layer, which rotates about the vertical axis, under the hypothesis of local thermal non-equilibrium, is analysed. Since the porosity of the medium is assumed to be high, the more suitable Darcy-Brinkman model is adopted. Linear instability analysis of the conduction solution is carried out. Nonlinear stability with respect to $$L^2$$ L 2 -norm is performed in order to prove the coincidence between the linear instability and the global nonlinear stability thresholds. The effect of both rotation and thermal and mechanical anisotropies on the critical Rayleigh number for the onset of instability is discussed.

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